Full-vectorial finite element method in a cylindrical coordinate system for loss analysis of photonic wire bends

This paper presents a new full-vectorial finite-element method in a local cylindrical coordinate system, to effectively analyze bending losses in photonic wires. The discretization is performed in the cross section of a three-dimensional curved waveguide, using hybrid edge/nodal elements. The solution region is truncated by anisotropic, perfectly matched layers in the cylindrical coordinate system, to deal properly with leaky modes of the waveguide. This approach is used to evaluate bending losses in silicon wire waveguides. The numerical results of the present approach are compared with results calculated with an equivalent straight waveguide approach and with reported experimental data. These comparisons together demonstrate the validity of the present approach based on the cylindrical coordinate system and also clarifies the limited validity of the equivalent straight waveguide approximation.